In this paper, we investigate the growth of solutions of the differential equations f^（k）+ A_k-1（z）f^（k-1）+ ··· + A₀（z）f = 0, where A_j（z）（j = 0, ···, k-1） are entire functions.When there exists some coefficient A_s（z）（s ∈ {1, ···, k-1}） being a nonzero solution of f’’+P（z）f = 0, where P（z） is a polynomial with degree n（≥ 1） and A₀（z） satisfies σ（A₀） ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order. 

In this paper, we investigate the growth of solutions of the differential equations f^（k）+ A_k-1（z）f^（k-1）+ ··· + A₀（z）f = 0, where A_j（z）（j = 0, ···, k-1） are entire functions.When there exists some coefficient A_s（z）（s ∈ {1, ···, k-1}） being a nonzero solution of f’’+P（z）f = 0, where P（z） is a polynomial with degree n（≥ 1） and A₀（z） satisfies σ（A₀） ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.